CS212:Data Structure

Transcription

1 C212:Data tructure

2 Direct applications Page-visited history in a Web browser Undo sequence in a text editor Chain of method calls in the Java Virtual Machine Indirect applications Auxiliary data structure for algorithms Component of other data structures Goodrich, Tamassia

3 The Java Virtual Machine (JVM) keeps track of the chain of active methods with a stack When a method is called, the JVM pushes on the stack a frame containing Local variables and return value Program counter, keeping track of the statement being executed When a method ends, its frame is popped from the stack and control is passed to the method on top of the stack Allows for recursion main() { int i = 5; foo(i); foo(int j) { int k; k = j+1; bar(k); bar(int m) { Goodrich, Tamassia

4 The Java Virtual Machine (JVM) keeps track of the chain of active methods with a stack When a method is called, the JVM pushes on the stack a frame containing Local variables and return value Program counter, keeping track of the statement being executed When a method ends, its frame is popped from the stack and control is passed to the method on top of the stack Allows for recursion main() { int i = 5; foo(i); foo(int j) { int k; k = j+1; bar(k); bar(int m) { main PC = 2 i = Goodrich, Tamassia

5 The Java Virtual Machine (JVM) keeps track of the chain of active methods with a stack When a method is called, the JVM pushes on the stack a frame containing Local variables and return value Program counter, keeping track of the statement being executed When a method ends, its frame is popped from the stack and control is passed to the method on top of the stack Allows for recursion main() { int i = 5; foo(i); foo(int j) { int k; k = j+1; bar(k); bar(int m) { foo PC = 3 j = 5 k = 6 main PC = 2 i = Goodrich, Tamassia

6 The Java Virtual Machine (JVM) keeps track of the chain of active methods with a stack When a method is called, the JVM pushes on the stack a frame containing Local variables and return value Program counter, keeping track of the statement being executed When a method ends, its frame is popped from the stack and control is passed to the method on top of the stack Allows for recursion main() { int i = 5; foo(i); foo(int j) { int k; k = j+1; bar(k); bar(int m) { bar PC = 1 m = 6 foo PC = 3 j = 5 k = 6 main PC = 2 i = Goodrich, Tamassia

7 The Java Virtual Machine (JVM) keeps track of the chain of active methods with a stack When a method is called, the JVM pushes on the stack a frame containing Local variables and return value Program counter, keeping track of the statement being executed When a method ends, its frame is popped from the stack and control is passed to the method on top of the stack Allows for recursion main() { int i = 5; foo(i); foo(int j) { int k; k = j+1; bar(k); bar(int m) { foo PC = 3 j = 5 k = 6 main PC = 2 i = Goodrich, Tamassia

8 The Java Virtual Machine (JVM) keeps track of the chain of active methods with a stack When a method is called, the JVM pushes on the stack a frame containing Local variables and return value Program counter, keeping track of the statement being executed When a method ends, its frame is popped from the stack and control is passed to the method on top of the stack Allows for recursion main() { int i = 5; foo(i); foo(int j) { int k; k = j+1; bar(k); bar(int m) { main PC = 2 i = Goodrich, Tamassia

9 The Java Virtual Machine (JVM) keeps track of the chain of active methods with a stack When a method is called, the JVM pushes on the stack a frame containing Local variables and return value Program counter, keeping track of the statement being executed When a method ends, its frame is popped from the stack and control is passed to the method on top of the stack Allows for recursion main() { int i = 5; foo(i); foo(int j) { int k; k = j+1; bar(k); bar(int m) { Goodrich, Tamassia

10 public class Tester { // other methods here public void intreverse(list<integer> l) { tack<integer> s = new tack<integer>(); l.findfirst(); while(!l.empty()) { s.push(l.retrieve()); l.remove(); while(!s.empty()) l.insert(s.pop()); 10

11 C public class Tester { // other methods here L public void intreverse(list<integer> l) { tack<integer> s = new tack<integer>(); l.findfirst(); while(!l.empty()) { s.push(l.retrieve()); l.remove(); while(!s.empty()) l.insert(s.pop()); 11

12 public class Tester { // other methods here L C public void intreverse(list<integer> l) { tack<integer> s = new tack<integer>(); l.findfirst(); while(!l.empty()) { s.push(l.retrieve()); l.remove(); while(!s.empty()) l.insert(s.pop()); T 12

13 public class Tester { // other methods here L C public void intreverse(list<integer> l) { tack<integer> s = new tack<integer>(); l.findfirst(); while(!l.empty()) { s.push(l.retrieve()); l.remove(); while(!s.empty()) l.insert(s.pop()); T 13

14 public class Tester { // other methods here L C public void intreverse(list<integer> l) { tack<integer> s = new tack<integer>(); l.findfirst(); while(!l.empty()) { s.push(l.retrieve()); l.remove(); while(!s.empty()) l.insert(s.pop()); 1 T 14

15 public class Tester { // other methods here L C 2 3 public void intreverse(list<integer> l) { tack<integer> s = new tack<integer>(); l.findfirst(); while(!l.empty()) { s.push(l.retrieve()); l.remove(); while(!s.empty()) l.insert(s.pop()); 1 T 15

16 public class Tester { // other methods here L C 2 3 public void intreverse(list<integer> l) { tack<integer> s = new tack<integer>(); l.findfirst(); while(!l.empty()) { s.push(l.retrieve()); l.remove(); 2 T while(!s.empty()) l.insert(s.pop()); 1 16

17 public class Tester { // other methods here L C 3 public void intreverse(list<integer> l) { tack<integer> s = new tack<integer>(); l.findfirst(); while(!l.empty()) { s.push(l.retrieve()); l.remove(); 2 T while(!s.empty()) l.insert(s.pop()); 1 17

18 public class Tester { // other methods here L C 3 public void intreverse(list<integer> l) { tack<integer> s = new tack<integer>(); l.findfirst(); while(!l.empty()) { s.push(l.retrieve()); l.remove(); 3 T 2 while(!s.empty()) l.insert(s.pop()); 1 18

19 C public class Tester { // other methods here L public void intreverse(list<integer> l) { tack<integer> s = new tack<integer>(); l.findfirst(); while(!l.empty()) { s.push(l.retrieve()); l.remove(); 3 T 2 while(!s.empty()) l.insert(s.pop()); 1 19

20 C public class Tester { // other methods here L public void intreverse(list<integer> l) { tack<integer> s = new tack<integer>(); l.findfirst(); while(!l.empty()) { s.push(l.retrieve()); l.remove(); 3 T 2 while(!s.empty()) l.insert(s.pop()); 1 20

21 C public class Tester { L 3 // other methods here public void intreverse(list<integer> l) { tack<integer> s = new tack<integer>(); l.findfirst(); while(!l.empty()) { s.push(l.retrieve()); l.remove(); 3 T 2 while(!s.empty()) l.insert(s.pop()); 1 21

22 C public class Tester { L 3 2 // other methods here public void intreverse(list<integer> l) { tack<integer> s = new tack<integer>(); l.findfirst(); while(!l.empty()) { s.push(l.retrieve()); l.remove(); 2 T while(!s.empty()) l.insert(s.pop()); 1 22

23 C public class Tester { L // other methods here public void intreverse(list<integer> l) { tack<integer> s = new tack<integer>(); l.findfirst(); while(!l.empty()) { s.push(l.retrieve()); l.remove(); while(!s.empty()) l.insert(s.pop()); 1 T 23

24 C public class Tester { L // other methods here public void intreverse(list<integer> l) { tack<integer> s = new tack<integer>(); l.findfirst(); while(!l.empty()) { s.push(l.retrieve()); l.remove(); while(!s.empty()) l.insert(s.pop()); T 24

25 Each (, {, or [ must be paired with a matching ),, or [ correct: ( )(( )){([( )]) correct: ((( )(( )){([( )]))) incorrect: )(( )){([( )]) incorrect: ({[ ]) incorrect: ( 2010 Goodrich, Tamassia 25

26 Algorithm ParenMatch(X, n): Input: An array X of n tokens, each of which is either a grouping symbol, a variable, an arithmetic operator, or a number Output: true if and only if all the grouping symbols in X match Let be an empty stack for i=0 to n-1 do if X[i] is an opening grouping symbol then.push(x[i]) else if X[i] is a closing grouping symbol then return false {nothing to match with if.pop() does not match the type of X[i] then return false {wrong type return true {every symbol matched else return false {some symbols were never matched 2010 Goodrich, Tamassia 26

27 (2+[3-5]*2) Algorithm ParenMatch(X, n): Input: An array X of n tokens, each of which is either a grouping symbol, a variable, an arithmetic operator, or a number Output: true if and only if all the grouping symbols in X match Let be an empty stack for i=0 to n-1 do if X[i] is an opening grouping symbol then.push(x[i]) else if X[i] is a closing grouping symbol then return false {nothing to match with if.pop() does not match the type of X[i] then return false {wrong type return true {every symbol matched else return false {some symbols were never matched 2010 Goodrich, Tamassia 27

28 (2+[3-5]*2) Algorithm ParenMatch(X, n): Input: An array X of n tokens, each of which is either a grouping symbol, a variable, an arithmetic operator, or a number Output: true if and only if all the grouping symbols in X match Let be an empty stack for i=0 to n-1 do if X[i] is an opening grouping symbol then.push(x[i]) else if X[i] is a closing grouping symbol then return false {nothing to match with if.pop() does not match the type of X[i] then return false {wrong type return true {every symbol matched else return false {some symbols were never matched ( 2010 Goodrich, Tamassia 28

29 (2+[3-5]*2) Algorithm ParenMatch(X, n): Input: An array X of n tokens, each of which is either a grouping symbol, a variable, an arithmetic operator, or a number Output: true if and only if all the grouping symbols in X match Let be an empty stack for i=0 to n-1 do if X[i] is an opening grouping symbol then.push(x[i]) else if X[i] is a closing grouping symbol then return false {nothing to match with if.pop() does not match the type of X[i] then return false {wrong type return true {every symbol matched else return false {some symbols were never matched [ ( 2010 Goodrich, Tamassia 29

30 (2+[3-5]*2) Algorithm ParenMatch(X, n): Input: An array X of n tokens, each of which is either a grouping symbol, a variable, an arithmetic operator, or a number Output: true if and only if all the grouping symbols in X match Let be an empty stack for i=0 to n-1 do if X[i] is an opening grouping symbol then.push(x[i]) else if X[i] is a closing grouping symbol then return false {nothing to match with if.pop() does not match the type of X[i] then return false {wrong type return true {every symbol matched else return false {some symbols were never matched [ ( 2010 Goodrich, Tamassia 30

31 (2+[3-5]*2) Algorithm ParenMatch(X, n): Input: An array X of n tokens, each of which is either a grouping symbol, a variable, an arithmetic operator, or a number Output: true if and only if all the grouping symbols in X match Let be an empty stack for i=0 to n-1 do if X[i] is an opening grouping symbol then.push(x[i]) else if X[i] is a closing grouping symbol then return false {nothing to match with if.pop() does not match the type of X[i] then return false {wrong type return true {every symbol matched else return false {some symbols were never matched ( 2010 Goodrich, Tamassia 31

32 (2+[3-5]*2) true Algorithm ParenMatch(X, n): Input: An array X of n tokens, each of which is either a grouping symbol, a variable, an arithmetic operator, or a number Output: true if and only if all the grouping symbols in X match Let be an empty stack for i=0 to n-1 do if X[i] is an opening grouping symbol then.push(x[i]) else if X[i] is a closing grouping symbol then return false {nothing to match with if.pop() does not match the type of X[i] then return false {wrong type return true {every symbol matched else return false {some symbols were never matched 2010 Goodrich, Tamassia 32

33 (6+[8+2)*1) Algorithm ParenMatch(X, n): Input: An array X of n tokens, each of which is either a grouping symbol, a variable, an arithmetic operator, or a number Output: true if and only if all the grouping symbols in X match Let be an empty stack for i=0 to n-1 do if X[i] is an opening grouping symbol then.push(x[i]) else if X[i] is a closing grouping symbol then return false {nothing to match with if.pop() does not match the type of X[i] then return false {wrong type return true {every symbol matched else return false {some symbols were never matched 2010 Goodrich, Tamassia 33

34 (6+[8+2)*1) Algorithm ParenMatch(X, n): Input: An array X of n tokens, each of which is either a grouping symbol, a variable, an arithmetic operator, or a number Output: true if and only if all the grouping symbols in X match Let be an empty stack for i=0 to n-1 do if X[i] is an opening grouping symbol then.push(x[i]) else if X[i] is a closing grouping symbol then return false {nothing to match with if.pop() does not match the type of X[i] then return false {wrong type return true {every symbol matched else return false {some symbols were never matched ( 2010 Goodrich, Tamassia 34

35 (6+[8+2)*1) Algorithm ParenMatch(X, n): Input: An array X of n tokens, each of which is either a grouping symbol, a variable, an arithmetic operator, or a number Output: true if and only if all the grouping symbols in X match Let be an empty stack for i=0 to n-1 do if X[i] is an opening grouping symbol then.push(x[i]) else if X[i] is a closing grouping symbol then return false {nothing to match with if.pop() does not match the type of X[i] then return false {wrong type return true {every symbol matched else return false {some symbols were never matched [ ( 2010 Goodrich, Tamassia 35

36 (6+[8+2)*1) false Algorithm ParenMatch(X, n): Input: An array X of n tokens, each of which is either a grouping symbol, a variable, an arithmetic operator, or a number Output: true if and only if all the grouping symbols in X match Let be an empty stack for i=0 to n-1 do if X[i] is an opening grouping symbol then.push(x[i]) else if X[i] is a closing grouping symbol then return false {nothing to match with if.pop() does not match the type of X[i] then return false {wrong type return true {every symbol matched else return false {some symbols were never matched [ ( 2010 Goodrich, Tamassia 36

37 (6+[8+2]*1 Algorithm ParenMatch(X, n): Input: An array X of n tokens, each of which is either a grouping symbol, a variable, an arithmetic operator, or a number Output: true if and only if all the grouping symbols in X match Let be an empty stack for i=0 to n-1 do if X[i] is an opening grouping symbol then.push(x[i]) else if X[i] is a closing grouping symbol then return false {nothing to match with if.pop() does not match the type of X[i] then return false {wrong type return true {every symbol matched else return false {some symbols were never matched 2010 Goodrich, Tamassia 37

38 (6+[8+2]*1 Algorithm ParenMatch(X, n): Input: An array X of n tokens, each of which is either a grouping symbol, a variable, an arithmetic operator, or a number Output: true if and only if all the grouping symbols in X match Let be an empty stack for i=0 to n-1 do if X[i] is an opening grouping symbol then.push(x[i]) else if X[i] is a closing grouping symbol then return false {nothing to match with if.pop() does not match the type of X[i] then return false {wrong type return true {every symbol matched else return false {some symbols were never matched ( 2010 Goodrich, Tamassia 38

39 (6+[8+2]*1 Algorithm ParenMatch(X, n): Input: An array X of n tokens, each of which is either a grouping symbol, a variable, an arithmetic operator, or a number Output: true if and only if all the grouping symbols in X match Let be an empty stack for i=0 to n-1 do if X[i] is an opening grouping symbol then.push(x[i]) else if X[i] is a closing grouping symbol then return false {nothing to match with if.pop() does not match the type of X[i] then return false {wrong type return true {every symbol matched else return false {some symbols were never matched [ ( 2010 Goodrich, Tamassia 39

40 (6+[8+2]*1 Algorithm ParenMatch(X, n): Input: An array X of n tokens, each of which is either a grouping symbol, a variable, an arithmetic operator, or a number Output: true if and only if all the grouping symbols in X match Let be an empty stack for i=0 to n-1 do if X[i] is an opening grouping symbol then.push(x[i]) else if X[i] is a closing grouping symbol then return false {nothing to match with if.pop() does not match the type of X[i] then return false {wrong type return true {every symbol matched else return false {some symbols were never matched [ ( 2010 Goodrich, Tamassia 40

41 (6+[8+2]*1 false Algorithm ParenMatch(X, n): Input: An array X of n tokens, each of which is either a grouping symbol, a variable, an arithmetic operator, or a number Output: true if and only if all the grouping symbols in X match Let be an empty stack for i=0 to n-1 do if X[i] is an opening grouping symbol then.push(x[i]) else if X[i] is a closing grouping symbol then return false {nothing to match with if.pop() does not match the type of X[i] then return false {wrong type return true {every symbol matched else return false {some symbols were never matched ( 2010 Goodrich, Tamassia 41

42 For fully-correct HTML, each <name> should pair with a matching </name> <body> <center> <h1> The Little Boat </h1> </center> <p> The storm tossed the little boat like a cheap sneaker in an old washing machine. The three drunken fishermen were used to such treatment, of course, but not the tree salesman, who even as a stowaway now felt that he had overpaid for the voyage.</p> <ol> <li> Will the salesman die? </li> <li> What color is the boat? </li> <li> And what about Naomi? </li> </ol> </body> The Little Boat The storm tossed the little boat like a cheap sneaker in an old washing machine. The three drunken fishermen were used to such treatment, of course, but not the tree salesman, who even as a stowaway now felt that he had overpaid for the voyage. 1. Will the salesman die? 2. What color is the boat? 3. And what about Naomi? 2010 Goodrich, Tamassia 42

43 import java.io.*; import java.util.canner; import net.datastructures.*; /** implified test of matching tags in an HTML document. */ public class HTML { /** trip the first and last characters off a <tag> string. */ public static tring stripends(tring t) { if (t.length() <= 2) return null; // this is a degenerate tag return t.substring(1, t.length() - 1); /** Test if a stripped tag string is empty or a true opening tag. */ public static boolean isopeningtag(tring tag) { return (tag.length() == 0) (tag.charat(0)!= '/'); /** Test if stripped tag1 matches closing tag2 (first character is '/'). */ public static boolean arematchingtags(tring tag1, tring tag2) { return tag1.equals(tag2.substring(1)); // test against name after '/' 2010 Goodrich, Tamassia 43

44 /** Test if every opening tag has a matching closing tag. */ public static boolean ishtmlmatched(tring[] tag) { tack<tring> = new Nodetack<tring>(); // tack for matching tags for (int i = 0; (i < tag.length) && (tag[i]!= null); i++) { if (isopeningtag(tag[i])).push(tag[i]); // opening tag; push it on the stack else { if (.isempty()) return false;// nothing to match if (!arematchingtags(.pop(), tag[i])) return false; // wrong match if(.isempty()) return true; // we matched everything return false; // we have some tags that never were matched 2010 Goodrich, Tamassia 44

45 public final static int CAPACITY = 1000; // Tag array size /* Parse an HTML document into an array of html tags */ public static tring[] parsehtml(canner s) { tring[] tag = new tring[capacity]; // our tag array (initially all null) int count = 0; // tag counter tring token; // token returned by the scanner s while (s.hasnextline()) { while ((token = s.findinline("<[^>]*>"))!= null) // find the next tag tag[count++] = stripends(token); // strip the ends off this tag s.nextline(); // go to the next line return tag; // our array of (stripped) tags public static void main(tring[] args) throws IOException { if (ishtmlmatched(parsehtml(new canner(ystem.in)))) ystem.out.println("the input file is a matched HTML document."); else ystem.out.println("the input file is not a matched HTML document."); 2010 Goodrich, Tamassia 45

46 14 3 * = (14 (3 * 2) ) + 7 Operator precedence * has precedence over +/ Associativity operators of the same precedence group evaluated from left to right Example: (x y) + z rather than x (y + z) Idea: push each operator on the stack, but first pop and perform higher and equal precedence operations tallmann 46

47 Two stacks: optk holds operators valtk holds values Use $ as special end of input token with lowest precedence Algorithm doop() x valtk.pop(); y valtk.pop(); op optk.pop(); valtk.push( y op x ) Algorithm repeatops( refop ): while ( valtk.size() > 1 prec(refop) prec(optk.top() ) doop() Algorithm EvalExp() Input: a stream of tokens representing an arithmetic expression (with numbers) Output: the value of the expression while there s another token z if isnumber(z) then else repeatops($); return valtk.top() valtk.push(z) repeatops(z); optk.push(z) 47

48 * Operator has lower precedence than +/ * * * $ $ 5 14 $ F 2010 tallmann 48